Problem: Solve for $c$. $5c+16.5=13.5+10c$ $c=$
We need to manipulate the equation to get $ c $ by itself. $\begin{aligned} 5c+16.5&=13.5+10c \\\\ 5c+16.5 {-10c} &= 13.5+10c{-10c} &&\gray{\text{Subtract 10c from each side.}}\\\\ -5c+16.5&=13.5 &&\gray{\text{Combine like terms.}}\\\\ -5c+16.5{-16.5} &= 13.5{-16.5} &&\gray{\text{Subtract 16.5 from each side.}}\\\\ -5c &=-3 &&\gray{\text{Combine like terms.}}\\\\ \dfrac{-5c}{{-5}} &= \dfrac{-3}{{-5}} &&\gray{\text{Divide each side by -5.}}\\\\ c &= {0.6} &&\gray{\text{Simplify.}}\\\\ \end{aligned}$ The answer: $c = { 0.6 }~~~~~~~~$ [Let's check our work!]